Location: Water Seven City Area
Participants: Zoro, Nami, Sanji, Robin
Reward: Zoro, Nami, Sanji, and Robin's Bond Art, Fire Element Jewelry
In order to make the Frayed Memory for this Memory Link appear you need to complete the main story events surrounding Water Seven. Once you've defeated Rob Lucci you'll unlock a bunch of side content in and around Water Seven, including Force of Happiness. Head to Elevator-Top Floor and look down the southern street to find the Frayed Memory.
Part 1
Zoro, Nami, Sanji, and Robin will appear in Hysteria this time, and after some arguing between the guys the team will spot the owner of the floating ring: A woman who's standing nearby. Her name is Emily, and she's waiting for her beloved, Garf, to come home. He disappeared, and the only clue Emily can provide is his association with merchants at the Sewage Treatment Plant.
Head northwest of Emily and into the Sewage Treatment Plant. A slew of clues will greet you upon arrival. Speak to the Large Merchant on the right side of the street from the entrance, the large man in the striped shirt further down the street, and the large woman in pink looking northwest. You'll be pointed to the Abandoned Factory to the north of the Sewage Treatment Plant.
Head straight north through Abandoned Factory. Once you cross a bridge you'll find two suspicious fellows, and one of them, Black Suit, will send a pack of Scoundrels out to attack the Straw Hats. They're your typical Bandit-type enemies, and not a big deal. Sanji will do the most damage during this battle. (I also received a Dramatic Scene that involved beating one of the sword-wielding Scoundrels with Zoro, though I'm not sure if it's standard or not. If so, do it for some extra experience.)
The team will learn that Garf is being held in the Sewer beneath Water Seven, though before they can learn anything else they'll be ejected from Hysteria.
Part 2
Use Yoisa Travel to enter the Sewer, then backtrack to the entry point with the Yagara that ferries you through a thin channel of water. The Frayed Memory is on the north end of the water. Pop inside and head inside to spot the mobsters on the lower level of the Sewer. Zoro will immediately get himself in trouble, and you'll need to battle Black Suit and more Scoundrels. Take out Black Suit before he can use a more powerful attack for additional experience.
Drop down to B2F of the Sewer after the fight and go through the door on your left to get at the remaining mobsters. At the beginning of the brawl that follows the quartet will learn Thunder Lance Flip Caliber Phoenix Shot. It should wipe out every enemy on the field. If not, mop up any stragglers. Speak to the man in green (Garf) after the fight to reunite him with Emily and end the Memory Link.